Residents said the one-storey Popular Clinic which had been receiving wounded anti-US fighters and civilians was hit overnight as US-led forces pressed into the city.
The residents said on Tuesday it was impossible to reach the clinic because of heavy bombing and US tanks in the area.
The clinic's telephones were no longer working.
An Iraqi journalist, Abu Bakr al-Dulaimi, told Aljazeera that the overnight bombings which continued for more than 10 hours targeted everything in the city including the hospital and houses as well as cars.
Al-Dulaimi said the hospital's staff, doctors and patients, have all fallen victim to the assault. He said such fierce bombings have not been witnessed since the Iran-Iraq war.
The US military said it had no immediate information on any attack on the clinic.
Fierce clashes erupted between American troops and anti-US fighters in the neighbourhoods of al-Askari, al-Jughaivi and al-Dhubat near the northern gate of the city, Aljazeera learned.
Residents said smoke was rising from the whole city as it shook to constant explosions. Civilians were huddled in their homes and there was no word on casualties.
A US tank company commander in Iraq said on Tuesday that guerrillas were putting up a strong fight in the Jolan district of north-west Falluja, which is a rebel stronghold.
"These people are hard-core. They are putting up a strong fight and I saw many of them on the street I was on," Captain Robert Bodisch said.
"A man pulled out from behind a wall and fired an RPG at my tank. I have to get another tank to go back in there," he said without giving details.
The agency also reported that a US helicopter had been shot down.
US and Iraqi troops killed at least
15 civilians on Monday
"I saw the helicopter collide with a rocket. It turned into a ball of fire and fell to the ground," said Reuters reporter Fadl al-Badrani. "There was smoke everywhere."
He said the helicopter crashed in the city's Jolan district. A US military spokesman, however, had denied the report.
An AFP reporter in Jolan said one building in every 10 had been flattened. As US-led troops closed in on the neighbourhood overnight, at least four 2000lb (900kg) bombs were dropped in the city's north-west.
US and Iraqi forces seized Falluja's main hospital, across the Euphrates river from the city centre, on Monday night hours before the main offensive got under way.
Sami al-Jumaili, a doctor at the hospital, who escaped arrest when it was taken, said the city was running out of medical supplies and only a few clinics remained open.
"There is not a single surgeon in Falluja. We had one ambulance hit by US fire and a doctor wounded. There are scores of injured civilians in their homes whom we can't move."
"A 13-year-old child just died in my hands," he told reporters by telephone from a house where he had gone to help the wounded.
Doctors said at least 15 civilians had been killed in Monday's fighting. There was no word on US casualties.
Iraq's US-backed interim government sees Falluja and its sister city of Ramadi as havens for anti-US fighters that must be retaken to allow nationwide elections to go ahead in January.
Residents say the whole city
shook to constant explosions
"We are determined to clean Falluja from the terrorists," interim Prime Minister Iyad Allawi said on Monday in Baghdad.
US Secretary of State Colin Powell echoed the theme.
"We have begun an operation in Falluja today to ... defeat this hornet's nest of insurgent activity and terrorist activity," he told reporters on his way to Mexico City.
Allawi declared a 60-day emergency rule from Sunday to help crush the "insurgency" and pave the way for elections. On Monday he used those powers to impose a curfew on Falluja and Ramadi, and effectively seal the borders with Jordan and Syria.
Islamic Party quits
The political cost of the operation is already beginning to mount.
A major Sunni political party has quit the interim US-backed Iraqi government and revoked its single minister from the cabinet in protest over the US in Falluja, the party's leader said on Tuesday.
"We are protesting the attack on Falluja and the injustice that is inflicted on the innocent people of the city," said Muhsin Abd al-Hamid, head of the Iraqi Islamic Party.
"We are protesting the attack on Falluja and the injustice that is inflicted on the innocent people of the city. We cannot be part of this attack"
Muhsin Abd al-Hamid
Head of the Iraqi Islamic Party
Abd al-Hamid said the party leaders convened on Monday and decided that their one minister in the cabinet - Minister of Industry Hashim al-Hasani - should quit.
"We cannot be part of this attack," the leader said.
In a statement to Aljazeera, the Islamic Party in Iraq accused the US-backed interim Iraqi government of allowing the killing of Iraqis.
The party called for the immediate halt to all bloodshed.
Another Sunni grouping, the Association of Muslim Scholars (AMS) urged the UN Secretary-General Kofi Annan and the Arab League secretary-general and "all those who live with a conscience around the world" to be aware of the "massacres and elimination war" in Falluja.
Dr Harith al-Dhari, secretary-general of the AMS, said the "Iraqi resistance" was a legitimate right.
Iyad Allawi has imposed a
60-day state of emergency
"The resistance has been legitimate since its first days. We only need to reconfirm this in order to expel the confusion caused by some external fatwas [Islamic decrees] prohibiting jihad."
Al-Dhari added: "Iraqis are in jihad as they have the right to defend themselves. This right is approved by all laws and heavenly religions.
"We have said we support the resistance since the occupation of this country began. This is our right as Iraqis. Therefore, we don't need a fatwa on this issue as this matter is clear," he added.
"This is a jihad of defence that needs no consultation or fatwas to be issued."